Harris Hawk optimization algorithm with combined perturbation strategy and its application

Solving complex engineering optimization problems can improve design quality, reduce costs, and enhance performance and reliability. However, these problems are often nonlinear, non-convex, and multimodal. The Harris Hawk Optimization (HHO) algorithm has limitations such as poor exploration-exploitation balance, tendency to fall into local optima, slow convergence, and low accuracy. To address these issues, this paper proposes an improved HHO algorithm with a combined perturbation strategy (HHO-CPS). First, an adaptive oscillatory escape energy parameter E formula is introduced to better improve the balance between exploration and exploitation in HHO by dynamically adjusting the energy value from large to small. Second, the improved position update formulas for exploration and exploitation phases in HHO-CPS address the limited offspring distribution range and underutilization of elite individual information. They fully utilize elite information and expand offspring distribution, increasing the likelihood of capturing prey and generating promising solutions. Additionally, the combined perturbation strategy not only enhances population diversity but also improves the algorithm's convergence speed. Finally, the effectiveness of HHO-CPS is verified by comparing it with eleven other algorithms from the literature using CEC 2017 (30-D, 50-D), CEC 2022 (10-D, 20-D), and four real-world engineering optimization problems. The test results, Friedman rank analysis, and Friedman test demonstrate that HHO-CPS significantly outperforms the other eleven algorithms in terms of both performance and robustness, with substantial differences in algorithm performance. The experimental results fully validate the effectiveness and feasibility of the HHO-CPS algorithm. In summary, HHO-CPS demonstrates great potential in solving complex engineering optimization problems and has a broad application prospect, which will contribute to the optimization and innovation of engineering design.